Calculate the sum of the geometric series $1+\left(\frac{1}{5}\right)+\left(\frac{1}{5}\right)^2 + \left(\frac{1}{5}\right)^3 + \dots$. Express your answer as a common fraction.
This is an infinite geometric series with first term $1$ and common ratio $1/5$. Thus, the sum is $\frac{1}{1-\frac15} = \boxed{\frac{5}{4}}$.